Page 113 - Modern physical chemistry

Questions 103

At constant entropy, an enthalpy loss makes AGT,P negative and so drives the given process.
When there is entropy change, TAB has the same effect in driving the process as a - MI
of the same size.
At the atomic level, an increase of entropy corresponds to an increase of state number
W, in effect, an increase in the freedom for the system. This increase in freedom can
counteract an increase in enthalpy energy H, following equation (5.117).

5.15 A Fourth Law
When the molecules of a system are distributed over the allowed states randomly, the
entropy S is related to the state number W by formula (5.55). In an ideal gas, the only
effect of the intermolecular interactions is to introduce this randomness. But when the
interactions have a restrictive effect on the translational motions of the molecules, the
result is similar to that produced by reducing the volume available. At a given tempera-
ture, this reduces the entropy, according to equation (5.26).
Consider a macroscopic system of molecules at temperature T in volume V. Suppose
that all parameters of each species of molecule present are known. Then one can cal-
culate the entropy Si' assuming there is no interaction between the molecules, but that
randomness prevails.
Any possible intermolecular interaction, attraction at large distances, repulsion at
small intermolecular distances, has the effect of introducing a restriction on the move-
ments of the molecules. As a result, it lowers the state number for formula (5.55). We
conclude that the ideal Si is an upper bound on the entropy.
This inference is embodied in the fourth law of thermodynamics: The entropy S of
a real system at a given T and V is less than it would be if the system behaved as an ideal
gas; we have
[5.118]
In section 7.7, we will calculate the difference Si - S for a nonideal gas at low pres-
sures. The ideal entropy Si can be calculated from molecular parameters using the Boltz-
mann distribution law. Molecular parameters may be determined from spectroscopic
measurements. Many may be calculated from first principles using quantum mechanics.

Questions
5.1 What empirical basis is there for the Caratheodory principle?
5.2 How does the Caratheodory principle allow one to correlate all macroscopic states of a
uniform system to the points on a straight line?
5.3 How does this correlation imply that an integrating factor exists for dqrev for the system?
5.4 What form does dwrev for a uniform system assume?
5.5 What form does dqrev for a uniform system assume?
5.6 How does this form allow one to construct a surface on which entropy S of the uniform
system is constant?
5.7 How may dqrev vary in going between neighboring points on two such neighboring surfaces?
5.8 How may the form for the integrating factor for dqrev be found?
5.9 Construct formulas for the change in entropy in standard processes.
5.10 How is energy disSipated in a spontaneous process?
5.11 How does such dissipation affect the formula for the entropy change in (a) the system, (b)
the system plus surroundings?
5.12 Show how the last inequality in (5.32) follows from the zeroth law.
5.13 Summarize the results obtained above in the second law of thermodynamics.
5.14 Derive the formula for the entropy of mixing.
5.15 Construct the corresponding expression for the probability change on mixing.